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Lines and Angles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
In the given figure, straight lines $AB$ and $CD$ interect at $O$.If $\angle\text{AOC}=\phi,\angle\text{BOC}=\theta$ and $\theta=3\phi,$ then $\phi=?$
  • A
    $30^\circ$
  • B
    $40^\circ$
  • ✓
    $45^\circ$
  • D
    $60^\circ$
✓

Answer

Correct option: C.
$45^\circ$
$\angle\text{AOD}=\angle\text{COB}=\theta$
$\angle\text{AOC}=\angle\text{BOD}=\phi$
Since the sum of the measures of the angles around a point is $360^\circ ,$
$\angle\text{AOD}+\angle\text{COB}+\angle\text{AOC}+\angle\text{BOD}=360^\circ$
$\Rightarrow\theta+\theta+\phi+\phi=360$
$\Rightarrow2(\theta+\phi)=360$
$\Rightarrow\theta+\phi=180$
Given that $\theta=3\phi.$
So, $3\phi+\phi=180$
$\Rightarrow4\phi=180$
$\Rightarrow\phi=45$

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